The propagation of stress wave has great influence on impact buckling of axial compression bar significantly. At present, correlation studies have not been involved with the reflection of stress wave at far-end in most cases, and fixed constraint is considered at axial stress wave front (fixed of wave front). This method could not take the unstressing part of bar and boundary condition of far-end into account for impact bifurcation buckling problem of bar, which is not uniform to theory completely. The dynamic bifurcation buckling of axial compression bars with different boundary conditions under step load are analyzed. Continuous of wave front is used to solve the problem more properly in place of fixed of wave front. Some calculation results about impact bifurcation buckling of elastic and elasto-plastic bars are obtained, and valuable conclusions are drawn.